Question: What do the following two equations represent? $3x-2y = -2$ $-6x+4y = -3$
Putting the first equation in $y = mx + b$ form gives: $3x-2y = -2$ $-2y = -3x-2$ $y = \dfrac{3}{2}x + 1$ Putting the second equation in $y = mx + b$ form gives: $-6x+4y = -3$ $4y = 6x-3$ $y = \dfrac{3}{2}x - \dfrac{3}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.